A typical form of rotary printing machine has at least one printing mechanism including a plate cylinder which can be releasably mounted to a shaft carrying it. The plate cylinder carries a printing plate which is fixedly connected thereto. If the printing plate is provided with the respective print image to be produced, in a special imaging or image-applying apparatus, that is to say outside the printing mechanism itself, it is then necessary for the printing or blanket cylinder, upon being fitted into the printing mechanism, to be properly oriented with respect to the shaft which carries it, in such a way that the print image which is transferred from the printing plate on to the printing cylinder is correctly oriented with respect to the article to which the printing is to be applied and on to which therefore the printing or blanket cylinder transfers the print image. In view of the fact that in many cases the number of articles to which printing is to be applied in the same fashion, that is to say the number of articles constituting a respective batch, may be very low, there is a need for the printing plate to be changed at short intervals of time. If the printing plate is fixedly connected to the plate cylinder, frequent changes in the printing plate entail correspondingly frequent changes in the plate cylinder. The amount of time that this involves is particularly significant when, as is normally always the case in offset printing, the article is to be successively provided with a plurality of partial print images each consisting of different colors or inks, which supplement each other to form an overall print image. This therefore requires a corresponding number of printing mechanisms and accordingly also plate cylinders, in the rotary printing machine.